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Mathematics LibreTexts

1.26: Solving Fractional Equations

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A fractional equation is an equation involving fractions which has the unknown in the denominator of one or more of its terms.

Example 24.1

The following are examples of fractional equations:

a) \(\frac{3}{x}=\frac{9}{20}\)

b) \(\frac{x-2}{x+2}=\frac{3}{5}\)

c) \(\frac{3}{x-3}=\frac{4}{x-5}\)

d) \(\frac{3}{4}-\frac{1}{8 x}=0\)

e) \(\frac{x}{6}-\frac{2}{3 x}=\frac{2}{3}\)

The Cross-Product property can be used to solve fractional equations.

Cross-Product Property

If \(\frac{A}{B}=\frac{C}{D}\) then \(A \cdot D=B \cdot C\).

Using this property we can transform fractional equations into non-fractional ones. We must take care when applying this property and use it only when there is a single fraction on each side of the equation. So, fractional equations can be divided into two categories.

I. Single Fractions on Each Side of the Equation

Equations a), b) and c) in Example 24.1 fall into this category. We solve these equations here.

a) Solve \(\frac{3}{x}=\frac{9}{20}\)

\[\begin{array}{ll} \text{Cross-Product} & 3 \cdot 20=9 \cdot x \\ \text{Linear Equation} & 60=9 x \\ \text{Divide by 9 both sides} & \frac{60}{9}=x \end{array}\nonumber\]

The solution is \(x=\frac{60}{9}=\frac{20}{3}\).

\[\begin{array}{ll} \text{Cross-Product} & 5 \cdot(x-2)=3 \cdot(x+2) \\ \text{Remove parentheses} & 5 x-10=3 x+6 \\ \text{Linear Equation: isolate the variable} & 5 x-3 x=10+6 \\ & 2 x=16 \\ \text{Divide by 2 both sides} & \frac{2 x}{2}=\frac{16}{2}\end{array}\nonumber\]

the solution is \(x=8\).

\[\begin{array}{ll} \text{Cross-Product} & 3 \cdot(x-5)=4 \cdot(x-3) \\ \text{Remove parentheses} & 3 x-15=4 x-12 \\ \text{Linear Equation: isolate the variable} & 3 x-4 x=15-12 \\ & -x=3 \\ \text{Divide by 2 both sides} & \frac{-x}{-1}=\frac{3}{-1}\end{array}\nonumber\]

The solution is \(x=-3\)

Note: If you have a fractional equation and one of the terms is not a fraction, you can always account for that by putting 1 in the denominator. For example:

\[\frac{3}{x}=15\nonumber\]

We re-write the equation so that all terms are fractions.

\[\frac{3}{x}=\frac{15}{1}\nonumber\]

\[\begin{array}{ll} \text{Cross-Product} & 3 \cdot 1=15 \cdot x \\ \text{Linear Equation: isolate the variable} & 3=15 x \\ \text{Divide by 15 both sides} & \frac{3}{15}=\frac{15 x}{15} \end{array}\nonumber\]

The solution is \(x=\frac{3}{15}=\frac{3 \cdot 1}{3 \cdot 5}=\frac{1}{5}\).

II. Multiple Fractions on Either Side of the Equation

Equations d) and e) in Example 24.1 fall into this category. We solve these equations here.

We use the technique for combining rational expressions we learned in Chapter 23 to reduce our problem to a problem with a single fraction on each side of the equation.

d) Solve \(\frac{3}{4}-\frac{1}{8 x}=0\)

First we realize that there are two fractions on the LHS of the equation and thus we cannot use the Cross-Product property immediately. To combine the LHS into a single fraction we do the following:

\[\begin{array}{ll} \text{Find the LCM of the denominators} & 8 x \\ \text{Rewrite each fraction using the LCM} & \frac{3 \cdot 2 x}{8 x}-\frac{1}{8 x}=0 \\ \text{Combine into one fraction} & \frac{6 x-1}{8 x}=0 \\ \text{Re-write the equation so that all terms are fractions} & \frac{6 x-1}{8 x}=\frac{0}{1} \\ \text{Cross-Product} & (6 x-1) \cdot 1=8 x \cdot 0 \\ \text{Remove parentheses} & 6 x-1=0 \\\text{Linear Equation: isolate the variable} & 6 x=1 \\ \text{Divide by 6 both sides} & \frac{6 x}{6}=\frac{1}{6} \end{array}\nonumber\]

The solution is \(x=\frac{1}{6}\).

e) Solve \(\frac{x}{6}+\frac{2}{3 x}=\frac{2}{3}\)

\[\begin{array}{ll} \text{Find the LCM of the denominators of LHS} & 6x \\ \text{Rewrite each fraction on LHS using their LCM} & \frac{x \cdot x}{6 x}+\frac{2 \cdot 2}{6 x}=\frac{2}{3} \\ \frac{x^{2}+4}{6 x}=\frac{2}{3} \text{Combine into one fraction} & \left(x^{2}+4\right) \cdot 3=6 x \cdot 2 \\ \text{Cross-Product} & 3 x^{2}+12=12 x \\ \text{Remove parentheses} & 3 x^{2}-12 x+12=0 \\ \text{Quadratic Equation: Standard form} & 3 x^{2}-12 x+12=0 \\\text{Quadratic Equation: Factor} & 3 \cdot x^{2}-3 \cdot 4 x+3 \cdot 4=0 \\ & 3\left(x^{2}-4 x+4\right)=0 \\ & 3(x-2)(x-2)=0 \\ \text{Divide by 3 both sides} & \frac{3(x-2)(x-2)}{3}=\frac{0}{3} \\ & (x-2)(x-2)=0 \\ \text{Quadratic Equation: Zero-Product Property} & (x-2)=0 \text { or }(x-2)=0 \end{array}\nonumber\]

Since both factors are the same, then \(x-2=0\) gives \(x=2\). The solution is \(x=2\)

Note: There is another method to solve equations that have multiple fractions on either side. It uses the LCM of all denominators in the equation. We demonstrate it here to solve the following equation: \(\frac{3}{2}-\frac{9}{2 x}=\frac{3}{5}\)

\[\begin{array} \text{Find the LCM of all denominators in the equation} & 10x \\ \text{Multiply every fraction (both LHS and RHS) by the LCM} & 10 x \cdot \frac{3}{2}-10 x \cdot \frac{9}{2 x}=10 x \cdot \frac{3}{5} \\ & \frac{10 x \cdot 3}{2}-\frac{10 x \cdot 9}{2 x}=\frac{10 x \cdot 3}{5} \\ \text{Simplify every fraction} & \frac{5 x \cdot 3}{1}-\frac{5 \cdot 9}{1}=\frac{2 x \cdot 3}{1} \\ \text{See how all denominatiors are now 1, thus can be disregarded} & 5 x \cdot 3-5 \cdot 9=2 x \cdot 3 \\ \text{Solve like you would any other equation} & 15 x-45=6 x \\ \text{Linear equation: islolate the variable} & 15 x-6 x=45 \\ & 9 x=45 \\ & x=\frac{45}{9} \\ & x=5 \end{array} \nonumber\]

The solution is \(x=5\)

Exit Problem

Solve: \(\frac{2}{x}+\frac{1}{3}=\frac{1}{2}\)

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How to Solve for X

Last Updated: February 14, 2024 Fact Checked

This article was co-authored by David Jia . David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. There are 8 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 785,511 times.

There are a number of ways to solve for x, whether you're working with exponents and radicals or if you just have to do some division or multiplication. No matter what process you use, you always have to find a way to isolate x on one side of the equation so you can find its value. Here's how to do it:

Using a Basic Linear Equation

Step 1 Write down the problem.

  • 2 2 (x+3) + 9 - 5 = 32

Step 2 Resolve the exponent.

  • 4(x+3) + 9 - 5 = 32

Step 3 Do the multiplication....

  • 4x + 12 + 9 - 5 = 32

Step 4 Do the addition...

  • 4x+21-5 = 32
  • 4x + 16 - 16 = 32 - 16

Step 5 Isolate the variable.

  • 4x/4 = 16/4

Step 6 Check your work.

  • 2 2 (x+3)+ 9 - 5 = 32
  • 2 2 (4+3)+ 9 - 5 = 32
  • 2 2 (7) + 9 - 5 = 32
  • 4(7) + 9 - 5 = 32
  • 28 + 9 - 5 = 32
  • 37 - 5 = 32

With Exponents

Step 1 Write down the problem.

  • 2x 2 + 12 = 44

Step 2 Isolate the term with the exponent.

  • 2x 2 +12-12 = 44-12

Step 3 Isolate the variable with the exponent by dividing both sides by the coefficient of the x term.

  • (2x 2 )/2 = 32/2
  • 4 Take the square root of each side of the equation. [6] X Research source Taking the square root of x 2 will cancel it out. So, take the square root of both sides. You'll get x left over on one side and plus or minus the square root of 16, 4, on the other side. Therefore, x = ±4.
  • 2(4) 2 + 12 = 44
  • 2(16) + 12 = 44
  • 32 + 12 = 44

Using Fractions

Step 1 Write down the problem.

  • (x + 3)/6 = 2/3

Step 2 Cross multiply...

  • (x + 3) x 3 = 3x + 9
  • 3x + 9 = 12

Step 3 Combine like terms.

  • 3x + 9 - 9 = 12 - 9

Step 4 Isolate x by dividing each term by the x coefficient.

  • (1 + 3)/6 = 2/3

Using Radical Signs

Step 1 Write down the problem.

  • √(2x+9) - 5 = 0

Step 2 Isolate the square root.

  • √(2x+9) - 5 + 5 = 0 + 5
  • √(2x+9) = 5

Step 3 Square...

  • (√(2x+9)) 2 = 5 2
  • 2x + 9 = 25

Step 4 Combine like terms.

  • 2x + 9 - 9 = 25 - 9

Step 5 Isolate the variable.

  • √(2(8)+9) - 5 = 0
  • √(16+9) - 5 = 0
  • √(25) - 5 = 0

Using Absolute Value

Step 1 Write down the problem.

  • |4x +2| - 6 = 8

Step 2 Isolate the absolute...

  • |4x +2| - 6 + 6 = 8 + 6
  • |4x +2| = 14

Step 3 Remove the absolute value and solve the equation.

  • 4x + 2 = 14
  • 4x + 2 - 2 = 14 -2

Step 4 Remove the absolute value and change the sign of the terms on the opposite side of the equal sign before you solve.

  • 4x + 2 = -14
  • 4x + 2 - 2 = -14 - 2
  • 4x/4 = -16/4

Step 5 Check your work.

  • |4(3) +2| - 6 = 8
  • |12 +2| - 6 = 8
  • |14| - 6 = 8
  • |4(-4) +2| - 6 = 8
  • |-16 +2| - 6 = 8
  • |-14| - 6 = 8

Practice Problems and Answers

solve for x fraction problems

Expert Q&A

David Jia

  • To check your work, plug the value of x back into the original equation and solve. Thanks Helpful 0 Not Helpful 0
  • Radicals, or roots, are another way of representing exponents. The square root of x = x^1/2. Thanks Helpful 0 Not Helpful 0

solve for x fraction problems

You Might Also Like

Calculate Frequency

  • ↑ David Jia. Academic Tutor. Expert Interview. 23 February 2021
  • ↑ http://tutorial.math.lamar.edu/Classes/Alg/SolveLinearEqns.aspx
  • ↑ https://www.purplemath.com/modules/solvelin.htm
  • ↑ https://sciencing.com/tips-for-solving-algebraic-equations-13712207.html
  • ↑ https://www.youtube.com/watch?v=LMS1NR4gZN8
  • ↑ https://www.mathsisfun.com/algebra/fractions-algebra.html
  • ↑ http://www.mathsisfun.com/algebra/radical-equations-solving.html
  • ↑ http://www.sosmath.com/algebra/solve/solve0/solve0.html

About This Article

David Jia

To solve for x in a basic linear equation, start by resolving the exponent using the order of operations. Then, isolate the variable to get your answer. To solve for x when the equation includes an exponent, start by isolating the term with the exponent. Then, isolate the variable with the exponent by dividing both sides by the coefficient of the x term to get your answer. If the equation has fractions, start by cross-multiplying the fractions. Then, combine like terms and isolate x by dividing each term by the x coefficient. If you want to learn how to solve for x if the equation has radicals or absolute values, keep reading the article! Did this summary help you? Yes No

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In order to access this I need to be confident with:

Inverse operations

Solve equations with fractions

Here you will learn about how to solve equations with fractions, including solving equations with one or more operations. You will also learn about solving equations with fractions where the unknown is the denominator of a fraction.

Students will first learn how to solve equations with fractions in 7th grade as part of their work with expressions and equations and expand that knowledge in 8th grade.

What are equations with fractions?

Equations with fractions involve solving equations where the unknown variable is part of the numerator and/or denominator of a fraction.

The numerator (top number) in a fraction is divided by the denominator (bottom number).

To solve equations with fractions, you will use the “balancing method” to apply the inverse operation to both sides of the equation in order to work out the value of the unknown variable.

The inverse operation of addition is subtraction.

The inverse operation of subtraction is addition.

The inverse operation of multiplication is division.

The inverse operation of division is multiplication.

For example,

\begin{aligned} \cfrac{2x+3}{5} \, &= 7\\ \colorbox{#cec8ef}{$\times \, 5$} \; & \;\; \colorbox{#cec8ef}{$\times \, 5$} \\\\ 2x+3&=35 \\ \colorbox{#cec8ef}{$-\,3$} \; & \;\; \colorbox{#cec8ef}{$- \, 3$} \\\\ 2x & = 32 \\ \colorbox{#cec8ef}{$\div \, 2$} & \; \; \; \colorbox{#cec8ef}{$\div \, 2$}\\\\ x & = 16 \end{aligned}

What are equations with fractions?

Common Core State Standards

How does this relate to 7th grade and 8th grade math?

  • Grade 7: Expressions and Equations (7.EE.A.1) Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
  • Grade 8: Expressions and Equations (8.EE.C.7) Solve linear equations in one variable.
  • Grade 8: Expressions and Equations (8.EE.C.7b) Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

How to solve equations with fractions

In order to solve equations with fractions:

Identify the operations that are being applied to the unknown variable.

Apply the inverse operations, one at a time, to both sides of the equation.

Write the final answer, checking that it is correct.

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Solve equations with fractions examples

Example 1: equations with one operation.

Solve for x \text{: } \cfrac{x}{5}=4 .

The unknown is x.

Looking at the left hand side of the equation, the x is divided by 5.

\cfrac{x}{5}

2 Apply the inverse operations, one at a time, to both sides of the equation.

The inverse of “dividing by 5 ” is “multiplying by 5 ”.

You will multiply both sides of the equation by 5.

Solve equations with fractions example 1

3 Write the final answer, checking that it is correct.

The final answer is x=20.

You can check the answer by substituting the answer back into the original equation.

\cfrac{20}{5}=20\div5=4

Example 2: equations with one operation

Solve for x \text{: } \cfrac{x}{3}=8 .

Looking at the left hand side of the equation, the x is divided by 3.

\cfrac{x}{3}

The inverse of “dividing by 3 ” is “multiplying by 3 ”.

You will multiply both sides of the equation by 3.

Solve equations with fractions example 2

The final answer is x=24.

\cfrac{24}{3}=24\div3=8

Example 3: equations with two operations

Solve for x \text{: } \cfrac{x \, + \, 1}{2}=7 .

Looking at the left hand side of the equation, 1 is added to x and then divided by 2 (the denominator of the fraction).

\cfrac{x \, + \, 1}{2}

First, clear the fraction by multiplying both sides of the equation by 2.

Then, subtract 1 from both sides.

Solve equations with fractions example 3

The final answer is x=13.

\cfrac{13 \, +1 \, }{2}=\cfrac{14}{2}=14\div2=7

Example 4: equations with two operations

Solve for x \text{: } \cfrac{x}{4}-2=3 .

Looking at the left hand side of the equation, x is divided by 4 and then 2 is subtracted.

\cfrac{x}{4}-2

First, add 2 to both sides of the equation.

Then, multiply both sides of the equation by 4.

Solve equations with fractions example 4

\cfrac{20}{4}-2=20\div4-2=5-2=3

Example 5: equations with three operations

Solve for x \text{: } \cfrac{3x}{5}+1=7 .

Looking at the left hand side of the equation, x is multiplied by 3, then divided by 5 , and then 1 is added.

\cfrac{3x}{5}+1

First, subtract 1 from both sides of the equation.

Then, multiply both sides of the equation by 5.

Finally, divide both sides by 3.

Solve equations with fractions example 5

The final answer is x=10.

\cfrac{3 \, \times \, 10}{5}+1=\cfrac{30}{5}+1=6+1=7

Example 6: equations with three operations

Solve for x \text{: } \cfrac{2x-1}{7}=3 .

Looking at the left hand side of the equation, x is multiplied by 2, then 1 is subtracted, and the last operation is divided by 7 (the denominator).

\cfrac{2x-1}{7}

First, multiply both sides of the equation by 7.

Next, add 1 to both sides.

Solve equations with fractions example 6

The final answer is x=11.

\cfrac{2 \, \times \, 11-1}{7}=\cfrac{22-1}{7}=\cfrac{21}{7}=3

Example 7: equations with the unknown as the denominator

Solve for x \text{: } \cfrac{24}{x}=6 .

Looking at the left hand side of the equation, x is the denominator. 24 is divided by x.

\cfrac{24}{x}

You need to multiply both sides of the equation by x.

Then, you can divide both sides by 6.

Solve equations with fractions example 7

The final answer is x=4.

\cfrac{24}{4}=24\div4=6

Example 8: equations with the unknown as the denominator

Solve for x \text{: } \cfrac{18}{x}-6=3 .

Looking at the left hand side of the equation, x is the denominator. 18 is divided by x , and then 6 is subtracted.

\cfrac{18}{x}-6

First, add 6 to both sides of the equation.

Then, multiply both sides of the equation by x.

Finally, divide both sides by 9.

Solve equations with fractions example 8

The final answer is x=2.

\cfrac{18}{2}-6=9-6=3

Teaching tips for solving equations with fractions

  • When students first start working through practice problems and word problems, provide step-by-step instructions to assist them with solving linear equations.
  • Introduce solving equations with fractions with one-step problems, then two-step problems, before introducing multi-step problems.
  • Students will need lots of practice with solving linear equations. These standards provide the foundation for work with future linear equations in Algebra I and II.
  • Provide opportunities for students to explain their thinking through writing. Ensure that they are using key vocabulary, such as, absolute value, coefficient, equation, common factors, inequalities, simplify, etc.

Easy mistakes to make

  • The solution to an equation can be any type of number The unknowns do not have to be integers (whole numbers and their negative opposites). The solutions can be fractions or decimals. They can also be positive or negative numbers.
  • The unknown of an equation can be on either side of the equation The unknown, represented by a letter, is often on the left hand side of the equations; however, it doesn’t have to be. It could also be on the right hand side of an equation.

Solve equations with fractions image 2

  • Lowest common denominator (LCD) It is common to get confused between solving equations involving fractions and adding and subtracting fractions. When adding and subtracting, you need to work out the lowest/least common denominator (sometimes called the least common multiple or LCM). When you solve equations involving fractions, multiply both sides of the equation by the denominator of the fraction.

Related math equations lessons

  • Math equations
  • Rearranging equations
  • How to find the equation of a line
  • Substitution
  • Linear equations
  • Writing linear equations
  • Solving equations
  • Identity math
  • One step equations

Practice solve equations with fractions questions

1. Solve: \cfrac{x}{6}=3

GCSE Quiz False

You will multiply both sides of the equation by 6, because the inverse of “dividing by 6 ” is “multiplying by 6 ”.

Solve equations with fractions practice question 1

The final answer is x = 18.

\cfrac{18}{6}=18 \div 6=3

2. Solve: \cfrac{x \, + \, 4}{2}=7

Then subtract 4 from both sides.

Solve equations with fractions practice question 2

The final answer is x = 10.

\cfrac{10 \, + \, 4}{2}=\cfrac{14}{2}=14 \div 2=7

3. Solve: \cfrac{x}{8}-5=1

First, add 5 to both sides of the equation.

Then multiply both sides of the equation by 8.

Solve equations with fractions practice question 3

The final answer is x = 48.

\cfrac{48}{8}-5=48 \div 8-5=1

4. Solve: \cfrac{3x \, + \, 2}{4}=2

First, multiply both sides of the equation by 4.

Next, subtract 2 from both sides.

Solve equations with fractions practice question 4

The final answer is x = 2.

\cfrac{3 \, \times \, 2+2}{4}=\cfrac{6 \, + \, 2}{4}=\cfrac{8}{4}=8 \div 4=2

5. Solve: \cfrac{4x}{7}-2=6

Then multiply both sides of the equation by 7.

Finally, divide both sides by 4.

Solve equations with fractions practice question 5

The final answer is x = 14.

\cfrac{4 \, \times \, 14}{7}-2=\cfrac{56}{7}-2=56 \div 7-2=6

6. Solve: \cfrac{42}{x}=7

Then you divide both sides by 7.

Solve equations with fractions practice question 6

The final answer is x = 6.

\cfrac{42}{6}=42 \div 6=7

Solve equations with fractions FAQs

Yes, you still follow the order of operations when solving equations with fractions. You will start with any operations in the numerator and follow PEMDAS (parenthesis, exponents, multiply/divide, add/subtract), followed by any operations in the denominator. Then you will solve the rest of the equation as usual.

The next lessons are

  • Inequalities
  • Types of graphs
  • Coordinate plane
  • Number patterns
  • Algebraic expressions
  • Fractions operations

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Solve for X Fraction Calculator

Get help from this instant and handy tool ie., Solve for X Fraction Calculator to find the x value in the fractions easily. Simply enter the input fraction values in the input field & avail the result in no time after clicking the calculate button.

Here are some samples of Solve for X Fraction calculations.

  • Solve for X in Fraction 8 / 9 = x / 7
  • Solve for X in Fraction 7 / 6 = x / 8
  • Solve for X in Fraction 4 / 5 = x / 6
  • Solve for X in Fraction 2 / 3 = x / 9
  • Solve for X in Fraction 3 / 2 = x / 4
  • Solve for X in Fraction 5 / 4 = x / 3
  • Solve for X in Fraction 6 / 7 = x / 2
  • Solve for X in Fraction 9 / 8 = x / 5
  • Solve for X in Fraction 3 / x = 3 / 40
  • Solve for X in Fraction 7 / x = 8 / 79
  • Solve for X in Fraction 6 / x = 2 / 49
  • Solve for X in Fraction 2 / x = 5 / 13
  • Solve for X in Fraction 5 / x = 9 / 21
  • Solve for X in Fraction 4 / x = 4 / 24
  • Solve for X in Fraction 8 / x = 6 / 50
  • Solve for X in Fraction 9 / x = 7 / 14
  • Solve for X in Fraction 7 / 8 = 32 / x
  • Solve for X in Fraction 3 / 4 = 19 / x
  • Solve for X in Fraction 5 / 2 = 49 / x
  • Solve for X in Fraction 6 / 9 = 26 / x
  • Solve for X in Fraction 9 / 6 = 75 / x
  • Solve for X in Fraction 2 / 5 = 25 / x
  • Solve for X in Fraction 4 / 3 = 60 / x
  • Solve for X in Fraction 8 / 7 = 95 / x
  • Solve for X in Fraction x / 9 = 30 / 22
  • Solve for X in Fraction x / 2 = 61 / 24
  • Solve for X in Fraction x / 4 = 12 / 47
  • Solve for X in Fraction x / 5 = 68 / 29
  • Solve for X in Fraction x / 3 = 78 / 20
  • Solve for X in Fraction x / 7 = 31 / 95
  • Solve for X in Fraction x / 8 = 39 / 91
  • Solve for X in Fraction x / 6 = 40 / 80

Solve for X Fraction Calculator: Do you feel worried when solving the value of X in Fractions? Then, don't worry at all, we have come up with the free online and handy tool ie., Solve for X Fractions Calculator. Make the most out of this Solve for X Fraction Calculator to find the value of X using a cross multiplication method. This calculator is designed in such a way that people can understand the concept behind the calculation of solving for X in Fractions effortlessly with the detailed Explanation.

How to Solve for X in Fractions Using Cross Multiplication?

Here is the method called cross-multiplication to solve for X in Fractions. We have compiled three simple steps to find the value of x in the fractions below. Follow the points clearly and make your calculations easy and faster by hand. The steps are as follows:

  • In the first step, you have to cross multiply the first and seconds fractions.
  • In the second step, solve the equation for X by multiplying the top and bottom of the second fraction by the denominator of the first fraction.
  • In the third/final step, simplify for X by canceling the denominator value on both sides to get the cross multiplied value as the result of X.

Get a comprehensive solution to your math problem on solve for X in the fractions with our Solve for X Fraction Calculator. Check out all of our online calculators on fractions from Onlinecalculator.guru & practice your math skills and understand the concept by providing a detailed explanation of the problem.

Question: Solve the value of x in the given fraction 8/5 = 6/x using cross-multiplication

Given equation is 8/5 = 6/x for solving x in the fraction

Now, we are going to solve the X value in the fraction by Cross Multiplication

At Step-1, cross multiply the fractions

⇒ 8/5 = 6/x

⇒ 8 × x = 5 × 6

At Step-2, Solve the equation for X

⇒ 8x = 5 × 6

⇒ x = 5 × 6 ÷ 8

Therefore, the value of x in the fraction 8/5 = 6/x is 3.75.

Solve for X Fraction Calculator

FAQs on Solve for X Fraction Calculator

1. What is meant by Cross Multiplication?

Cross multiplication is the process of multiplying the numerator of one side to the denominator of the other side, effectively crossing the terms over.

2. What is the standard form to represent the cross-multiplication?

If the equation between two fractions is given in the form a/b = c/d then ad = bc or a = bc/d is the cross multiplication standard form of expression.

3. How do you solve for x in Fractions easily?

By using the Solve for X Fraction Calculator, you can easily solve the x value in the given fractions also you can learn the concept behind the calculation with illustrated show work.

4. Where should I get the detailed procedure on solving the X in Fractions using Cross Multiplication?

You can definitely get the detailed procedure on solving the X in Fractions using Cross Multiplication on our page.

Solving Equations

What is an equation.

An equation says that two things are equal. It will have an equals sign "=" like this:

That equations says:

what is on the left (x − 2)  equals  what is on the right (4)

So an equation is like a statement " this equals that "

What is a Solution?

A Solution is a value we can put in place of a variable (such as x ) that makes the equation true .

Example: x − 2 = 4

When we put 6 in place of x we get:

which is true

So x = 6 is a solution.

How about other values for x ?

  • For x=5 we get "5−2=4" which is not true , so x=5 is not a solution .
  • For x=9 we get "9−2=4" which is not true , so x=9 is not a solution .

In this case x = 6 is the only solution.

You might like to practice solving some animated equations .

More Than One Solution

There can be more than one solution.

Example: (x−3)(x−2) = 0

When x is 3 we get:

(3−3)(3−2) = 0 × 1 = 0

And when x is 2 we get:

(2−3)(2−2) = (−1) × 0 = 0

which is also true

So the solutions are:

x = 3 , or x = 2

When we gather all solutions together it is called a Solution Set

The above solution set is: {2, 3}

Solutions Everywhere!

Some equations are true for all allowed values and are then called Identities

Example: sin(−θ) = −sin(θ) is one of the Trigonometric Identities

Let's try θ = 30°:

sin(−30°) = −0.5 and

−sin(30°) = −0.5

So it is true for θ = 30°

Let's try θ = 90°:

sin(−90°) = −1 and

−sin(90°) = −1

So it is also true for θ = 90°

Is it true for all values of θ ? Try some values for yourself!

How to Solve an Equation

There is no "one perfect way" to solve all equations.

A Useful Goal

But we often get success when our goal is to end up with:

x = something

In other words, we want to move everything except "x" (or whatever name the variable has) over to the right hand side.

Example: Solve 3x−6 = 9

Now we have x = something ,

and a short calculation reveals that x = 5

Like a Puzzle

In fact, solving an equation is just like solving a puzzle. And like puzzles, there are things we can (and cannot) do.

Here are some things we can do:

  • Add or Subtract the same value from both sides
  • Clear out any fractions by Multiplying every term by the bottom parts
  • Divide every term by the same nonzero value
  • Combine Like Terms
  • Expanding (the opposite of factoring) may also help
  • Recognizing a pattern, such as the difference of squares
  • Sometimes we can apply a function to both sides (e.g. square both sides)

Example: Solve √(x/2) = 3

And the more "tricks" and techniques you learn the better you will get.

Special Equations

There are special ways of solving some types of equations. Learn how to ...

  • solve Quadratic Equations
  • solve Radical Equations
  • solve Equations with Sine, Cosine and Tangent

Check Your Solutions

You should always check that your "solution" really is a solution.

How To Check

Take the solution(s) and put them in the original equation to see if they really work.

Example: solve for x:

2x x − 3 + 3 = 6 x − 3     (x≠3)

We have said x≠3 to avoid a division by zero.

Let's multiply through by (x − 3) :

2x + 3(x−3) = 6

Bring the 6 to the left:

2x + 3(x−3) − 6 = 0

Expand and solve:

2x + 3x − 9 − 6 = 0

5x − 15 = 0

5(x − 3) = 0

Which can be solved by having x=3

Let us check x=3 using the original question:

2 × 3 3 − 3 + 3  =   6 3 − 3

Hang On: 3 − 3 = 0 That means dividing by Zero!

And anyway, we said at the top that x≠3 , so ...

x = 3 does not actually work, and so:

There is No Solution!

That was interesting ... we thought we had found a solution, but when we looked back at the question we found it wasn't allowed!

This gives us a moral lesson:

"Solving" only gives us possible solutions, they need to be checked!

  • Note down where an expression is not defined (due to a division by zero, the square root of a negative number, or some other reason)
  • Show all the steps , so it can be checked later (by you or someone else)

Solve for x Calculator

Enter the Equation you want to solve into the editor.

Please ensure that your password is at least 8 characters and contains each of the following:

  • a special character: @$#!%*?&

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Online Integral Calculator

Solve integrals with wolfram|alpha.

  • Natural Language

More than just an online integral solver

Wolfram|Alpha is a great tool for calculating antiderivatives and definite integrals, double and triple integrals, and improper integrals. The Wolfram|Alpha Integral Calculator also shows plots, alternate forms and other relevant information to enhance your mathematical intuition.

Integral results with plots, alternate forms, series expansions and answers

Learn more about:

Tips for entering queries

Use Math Input above or enter your integral calculator queries using plain English. To avoid ambiguous queries, make sure to use parentheses where necessary. Here are some examples illustrating how to ask for an integral using plain English.

  • integrate x/(x-1)
  • integrate x sin(x^2)
  • integrate x sqrt(1-sqrt(x))
  • integrate x/(x+1)^3 from 0 to infinity
  • integrate 1/(cos(x)+2) from 0 to 2pi
  • integrate x^2 sin y dx dy, x=0 to 1, y=0 to pi
  • View more examples

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Get immediate feedback and guidance with step-by-step solutions for integrals and Wolfram Problem Generator

Step-by-step solutions for integrals with detailed breakdowns and unlimited Wolfram Problem Generator eigenvalue practice problems

  • Step-by-step solutions
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What are integrals?

Integration is an important tool in calculus that can give an antiderivative or represent area under a curve..

The indefinite integral of , denoted , is defined to be the antiderivative of . In other words, the derivative of is . Since the derivative of a constant is 0, indefinite integrals are defined only up to an arbitrary constant. For example, , since the derivative of is . The definite integral of from to , denoted , is defined to be the signed area between and the axis, from to .

Both types of integrals are tied together by the fundamental theorem of calculus. This states that if is continuous on and is its continuous indefinite integral, then . This means . Sometimes an approximation to a definite integral is desired. A common way to do so is to place thin rectangles under the curve and add the signed areas together. Wolfram|Alpha can solve a broad range of integrals

How Wolfram|Alpha calculates integrals

Wolfram|Alpha computes integrals differently than people. It calls Mathematica's Integrate function, which represents a huge amount of mathematical and computational research. Integrate does not do integrals the way people do. Instead, it uses powerful, general algorithms that often involve very sophisticated math. There are a couple of approaches that it most commonly takes. One involves working out the general form for an integral, then differentiating this form and solving equations to match undetermined symbolic parameters. Even for quite simple integrands, the equations generated in this way can be highly complex and require Mathematica's strong algebraic computation capabilities to solve. Another approach that Mathematica uses in working out integrals is to convert them to generalized hypergeometric functions, then use collections of relations about these highly general mathematical functions.

While these powerful algorithms give Wolfram|Alpha the ability to compute integrals very quickly and handle a wide array of special functions, understanding how a human would integrate is important too. As a result, Wolfram|Alpha also has algorithms to perform integrations step by step. These use completely different integration techniques that mimic the way humans would approach an integral. This includes integration by substitution, integration by parts, trigonometric substitution and integration by partial fractions.

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Computer Science > Artificial Intelligence

Title: geoeval: benchmark for evaluating llms and multi-modal models on geometry problem-solving.

Abstract: Recent advancements in Large Language Models (LLMs) and Multi-Modal Models (MMs) have demonstrated their remarkable capabilities in problem-solving. Yet, their proficiency in tackling geometry math problems, which necessitates an integrated understanding of both textual and visual information, has not been thoroughly evaluated. To address this gap, we introduce the GeoEval benchmark, a comprehensive collection that includes a main subset of 2000 problems, a 750 problem subset focusing on backward reasoning, an augmented subset of 2000 problems, and a hard subset of 300 problems. This benchmark facilitates a deeper investigation into the performance of LLMs and MMs on solving geometry math problems. Our evaluation of ten LLMs and MMs across these varied subsets reveals that the WizardMath model excels, achieving a 55.67\% accuracy rate on the main subset but only a 6.00\% accuracy on the challenging subset. This highlights the critical need for testing models against datasets on which they have not been pre-trained. Additionally, our findings indicate that GPT-series models perform more effectively on problems they have rephrased, suggesting a promising method for enhancing model capabilities.

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  6. ADVANCED FRACTION MATH PROBLEMS / MATH TUTORIAL

COMMENTS

  1. Fractions Solve for Unknown X

    Answer: x = 15 Solution by Cross Multiplication For the equation 5 8 = x 24 5 8 = x 24 The cross product is 5 × 24 = 8 × x 5 × 24 = 8 × x Solving for x x = 5 × 24 8 x = 5 × 24 8 and reducing x = 15 x = 15 Solution by Proportion Since the equation is an equality If 24 ÷ 8 = 3 Then it is true that x ÷ 5 = 3 Solving for x x = 5 × 3 x = 15

  2. Solve For x Calculator

    To solve the equation for different variables step-by-step clear any fractions by multiplying both sides of the equation by the LCM of the denominators. Get all the terms with the wanted variable on one side of the equation and all the other terms on the other side.

  3. Fractions

    Quiz 124 − 79 124 ÷ 89 124 + 89 × 315 − 1026 Learn about fractions using our free math solver with step-by-step solutions.

  4. Fractions Calculator

    Free Fractions calculator - Add, Subtract, Reduce, Divide and Multiply fractions step-by-step

  5. 4.9: Solving Equations with Fractions

    Solution. Multiply both sides of the equation by the least common denominator for the fractions that appear in the equation. − 8 9x = 5 18 Original equation. 18( − 8 9x) = 18( 5 18) Multiply both sides by 18. − 16x = 5 On each side, cancel and multiply. 18( − 8 9) = − 16 and 18( 5 18) = 5.

  6. 1.26: Solving Fractional Equations

    The solution is \ (x=-3\) Note: If you have a fractional equation and one of the terms is not a fraction, you can always account for that by putting 1 in the denominator. For example: Solve. \ [\frac {3} {x}=15\nonumber\] We re-write the equation so that all terms are fractions. \ [\frac {3} {x}=\frac {15} {1}\nonumber\]

  7. Equation with variables on both sides: fractions

    To solve the equation (3/4)x + 2 = (3/8)x - 4, we first eliminate fractions by multiplying both sides by the least common multiple of the denominators. Then, we add or subtract terms from both sides of the equation to group the x-terms on one side and the constants on the other. Finally, we solve and check as normal.

  8. Fraction Calculator & Problem Solver

    Linear equations 1 Solve for x: 4x=3 4x= 3 See answer › Linear equations 2 Solve for x: \frac {2x} {3}+5= x-\frac {9} {2} 32x +5 = x− 29 See answer › Systems of equations 1 Solve the system:

  9. Fraction Calculator

    Fraction Calculator is a calculator that gives step-by-step help on fraction problems. Try it now. To enter a fraction, type a / in between the numerator and denominator. For example: 1/3 Or click the example. Example (Click to try) 1/3 + 1/4 Fractions Video Lesson. Khan Academy Video: Adding Fractions; Need more problem types?

  10. Fraction Calculator

    Get full access to all Solution Steps for any math problem By continuing, you ... For a Free Trial, Download The App. Physics; Chemistry; Math; Statistics; Geometry; Finance; Personal Finance; ... Binary Calculator. Graphing. Plot and analyze functions and equations with detailed steps. Study Tools AI Math Solver Popular Problems Study Guides ...

  11. Step-by-Step Math Problem Solver

    Example: 2x-1=y,2y+3=x What can QuickMath do? QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students. The algebra section allows you to expand, factor or simplify virtually any expression you choose.

  12. Microsoft Math Solver

    Online math solver with free step by step solutions to algebra, calculus, and other math problems. Get help on the web or with our math app.

  13. 3 Ways to Solve Fraction Questions in Math

    1 Add fractions with the same denominator by combining the numerators. To add fractions, they must have the same denominator. If they do, simply add the numerators together. [2] For instance, to solve 5/9 + 1/9, just add 5 + 1, which equals 6. The answer, then, is 6/9 which can be reduced to 2/3. 2

  14. Fractions Calculator

    This is a fraction calculator with steps shown in the solution. If you have negative fractions insert a minus sign before the numerator. So if one of your fractions is -6/7, insert -6 in the numerator and 7 in the denominator. Sometimes math problems include the word "of," as in What is 1/3 of 3/8?

  15. 6 Ways to Solve for X

    1 Write down the problem. Here it is: 2 2 (x+3) + 9 - 5 = 32 2 Resolve the exponent. Remember the order of operations: PEMDAS, which stands for Parentheses, Exponents, Multiplication/Division, and Addition/Subtraction. [1] You can't resolve the parentheses first because x is in the parentheses, so you should start with the exponent, 2 2. 2 2 = 4

  16. Solve Equations with Fractions

    Example 1: equations with one operation. Solve for x \text {: } \cfrac {x} {5}=4 x: 5x = 4. Identify the operations that are being applied to the unknown variable. The unknown is x. x. Looking at the left hand side of the equation, the x x is divided by 5. 5. \cfrac {x} {5} 5x. 2 Apply the inverse operations, one at a time, to both sides of the ...

  17. Solve for X Fraction Calculator

    Here are some samples of Solve for X Fraction calculations. Solve for X in Fraction 8 9 = x 7 Solve for X in Fraction 7 6 = x 8 Solve for X in Fraction 4 5 = x 6 Solve for X in Fraction 2 3 = x 9 Solve for X in Fraction 3 2 = x 4 Solve for X in Fraction 5 4 = x 3 Solve for X in Fraction 6 7 = x 2 Solve for X in Fraction 9 8 = x 5

  18. Solve

    Differentiation dxd (x − 5)(3x2 − 2) Integration ∫ 01 xe−x2dx Limits x→−3lim x2 + 2x − 3x2 − 9 Online math solver with free step by step solutions to algebra, calculus, and other math problems. Get help on the web or with our math app.

  19. Solving Equations

    In fact, solving an equation is just like solving a puzzle. And like puzzles, there are things we can (and cannot) do. Here are some things we can do: Add or Subtract the same value from both sides. Clear out any fractions by Multiplying every term by the bottom parts. Divide every term by the same nonzero value.

  20. Mathway

    Free math problem solver answers your algebra homework questions with step-by-step explanations.

  21. Solve for x Calculator

    Algebra Solve for x Calculator Step 1: Enter the Equation you want to solve into the editor. The equation calculator allows you to take a simple or complex equation and solve by best method possible. Step 2: Click the blue arrow to submit and see the result!

  22. Integral Calculator: Integrate with Wolfram|Alpha

    Use Math Input above or enter your integral calculator queries using plain English. To avoid ambiguous queries, make sure to use parentheses where necessary. Here are some examples illustrating how to ask for an integral using plain English. integrate x/(x-1) integrate x sin(x^2) integrate x sqrt(1-sqrt(x)) integrate x/(x+1)^3 from 0 to infinity

  23. [2402.10104] GeoEval: Benchmark for Evaluating LLMs and Multi-Modal

    Recent advancements in Large Language Models (LLMs) and Multi-Modal Models (MMs) have demonstrated their remarkable capabilities in problem-solving. Yet, their proficiency in tackling geometry math problems, which necessitates an integrated understanding of both textual and visual information, has not been thoroughly evaluated. To address this gap, we introduce the GeoEval benchmark, a ...

  24. Step-by-Step Calculator

    Symbolab is the best step by step calculator for a wide range of physics problems, including mechanics, electricity and magnetism, and thermodynamics. It shows you the steps and explanations for each problem, so you can learn as you go. How to solve math problems step-by-step?

  25. Revisiting the Dynamics of Two-Body Problem in the Framework of the

    In this analytical study, a novel solving method for determining the precise coordinates of a mass point in orbit around a significantly more massive primary body, operating within the confines of the restricted two-body problem (R2BP), has been introduced. Such an approach entails the utilization of a continued fraction potential diverging from the conventional potential function used in ...

  26. Mixed Fractions

    373. 121 +354. 121 ×354. Learn about mixed fractions using our free math solver with step-by-step solutions.